Question

The following table gives the lifetimes of 500 CFL lamps.

Lifetime (months)	9	10	11	12	13	14	more than 14
Number of Lamps	26	71	82	102	89	77	43

A bulb is selected at random. Find the probability that the lifetime of the selected bulb is less than 12 months.
A) $ \dfrac{{281}}{{500}} $
B) $ \dfrac{{81}}{{500}} $
C) $ \dfrac{{21}}{{500}} $
D) None of these

Answer 1

Hint: The probability that the lifetime of the bulb is less than 12 months will include all the CFL lamps that worked for less than 12 months. The probability will be the ratio of the sum of all bulbs which lasted less than 12 months to the total number of bulbs.

Complete step by step answer
Before calculating the probability that a bulb randomly chosen has a lifetime of fewer than 12 months, we need to calculate how many bulbs in the data given to us had a lifetime of fewer than 12 months.
So, the number of bulbs that will have a lifetime less than 12 months will be all the bulbs that had a lifetime of 9,10 or 11 months so they can be calculated as:
 $\Rightarrow n = 26 + 71 + 82 $
 $\Rightarrow 179 $
Then the probability that a bulb selected at random will have a lifetime less than 12 months will be the ratio of the bulbs that have a lifetime of fewer than 12 months (281) to the total number of bulbs (500). So, we can calculate the probability $ P $ as
 $ P = \dfrac{{179}}{{500}} $ .
Since none of the options in the question match the solution, the correct choice is an option (D).

Note
Since the question has asked to measure the probability that a selected bulb should have a lifetime of fewer than 12 months, we should not count the bulbs that have a lifetime of exactly 12 months but should only count those with a lifetime of less than 12 months. If we count the bulbs that have a lifetime of 12 months, the probability would come out to be $ 281/500 $ which corresponds to option (A) but is the wrong choice.